A387728 Numbers k such that the powerful part of the sum of divisors of k (A387726) is less than k.

2, 4, 5, 6, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 23, 24, 25, 26, 27, 28, 29, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 47, 48, 49, 50, 52, 53, 54, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 67, 68, 69, 72, 73, 74, 75, 76, 77, 78, 79, 80, 82, 83, 84, 86, 87, 88, 89, 90, 91, 92, 95, 96, 97

Offset

1,1

Links

Antti Karttunen, Table of n, a(n) for n = 1..10000

Index entries for sequences related to sigma(n).

Mathematica

A387728Q[k_] := Times @@ Power @@@ Select[FactorInteger[DivisorSigma[1, k]], Last[#] > 1 &] < k;
Select[Range[100], A387728Q] (* Paolo Xausa, Sep 13 2025 *)

Prog

(PARI)
A057521(n) = { my(f=factor(n)); prod(i=1, #f~, if(f[i, 2]>1, f[i, 1]^f[i, 2], 1)); };
A387726(n) = A057521(sigma(n));
is_A387728(n) = (A387726(n) < n);

Crossrefs

Cf. A000203, A057521, A387726, A387727 (complement).

Sequence in context: A133398 A138836 A175431 * A059921 A062289 A172284

Adjacent sequences: A387725 A387726 A387727 * A387729 A387730 A387731

Keyword

nonn

Author

Antti Karttunen, Sep 12 2025

Status

approved